simple_min_cost_flow_program.py

#!/usr/bin/env python3
# Copyright 2010-2021 Google LLC
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
#     http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
# [START program]
"""From Bradley, H. and M., 'Applied Mathematical Programming', figure 8.1."""
# [START import]
from ortools.graph import pywrapgraph
# [END import]


def main():
    """MinCostFlow simple interface example."""
    # [START data]
    # Define four parallel arrays: sources, destinations, capacities,
    # and unit costs between each pair. For instance, the arc from node 0
    # to node 1 has a capacity of 15.
    start_nodes = [0, 0, 1, 1, 1, 2, 2, 3, 4]
    end_nodes = [1, 2, 2, 3, 4, 3, 4, 4, 2]
    capacities = [15, 8, 20, 4, 10, 15, 4, 20, 5]
    unit_costs = [4, 4, 2, 2, 6, 1, 3, 2, 3]

    # Define an array of supplies at each node.
    supplies = [20, 0, 0, -5, -15]
    # [END data]

    # [START constraints]
    # Instantiate a SimpleMinCostFlow solver.
    min_cost_flow = pywrapgraph.SimpleMinCostFlow()

    # Add each arc.
    for arc in zip(start_nodes, end_nodes, capacities, unit_costs):
        min_cost_flow.AddArcWithCapacityAndUnitCost(arc[0], arc[1], arc[2],
                                                    arc[3])

    # Add node supplies.
    for count, supply in enumerate(supplies):
        min_cost_flow.SetNodeSupply(count, supply)
    # [END constraints]

    # [START solve]
    # Find the min cost flow.
    solve_status = min_cost_flow.Solve()
    # [END solve]

    # [START print_solution]
    if solve_status == min_cost_flow.OPTIMAL:
        print('Minimum cost: ', min_cost_flow.OptimalCost())
        print('')
        print(' Arc   Flow / Capacity  Cost')
        for i in range(min_cost_flow.NumArcs()):
            cost = min_cost_flow.Flow(i) * min_cost_flow.UnitCost(i)
            print('%1s -> %1s    %3s   / %3s   %3s' %
                  (min_cost_flow.Tail(i), min_cost_flow.Head(i),
                   min_cost_flow.Flow(i), min_cost_flow.Capacity(i), cost))
    else:
        print('Solving the min cost flow problem failed. Solver status: ',
              solve_status)
    # [END print_solution]


if __name__ == '__main__':
    main()
# [END program]